Leipzig is also in the Bundesliga not in La Liga and I think you are a little mistaken in this regard and for Stuttgart they just need to maintain their own position until the end of the season by continuing to win in every remaining game. And at least Stuttgart can be in that position in order to enter the Champions League competition next season, because Leipzig is still hindered by Dortmund in terms of fighting for the top four positions in the Bundesliga standings.
In the next match, Stuttgart will meet Heidenheim and in my opinion this will be an easy match for Stuttgart to win at the end of the month, at least Stuttgart needs two wins to take second place from Bayern Munich and I am very confident that Stuttgart is capable of doing that.
Stuttgart should worry more about staying in the third place rather than fighting Bayern Munich. I mean having a good ambition is something that every team should have but right now and after several mistakes, they found themselves third and risking to lose it in the upcoming rounds if they got a negative result.
Their next game will be against Heidenheim which should not be that hard. The match after will be against Borussia Dortmund were the gap risk to shrink between these two teams!